The present invention relates to methods for modeling the quality and performance of a reservoir that contains hydrocarbon fluids, and more particularly, to methods for predicting the flow characteristics of a reservoir of hydrocarbon fluids. Still more particularly, the present invention relates to a method for identifying and characterizing units of a formation having similar hydraulic characteristics based on microscopic measurements of rock core samples and for linking the hydraulic units to wireline logs to enable accurate prediction of formation flow characteristics therefrom.
Traditional techniques for making macroscopic measurements of reservoir characteristics, like wireline logs, are unable to measure reservoir dynamic functions, such as formation permeability. Instead, reservoir engineers must rely on microscopic measurements of permeability derived from data obtained on core samples and on empirical or regressional correlations between permeability and log-derived porosity measurements to predict formation permeability. Permeability measurements derived from core samples are accurate and give precise inch by inch or foot by foot descriptions of formation permeability, but are difficult to scale to reservoir size. Quantitative correlations between porosity and permeability are not satisfactory due to the absence of a suitable transform for predicting permeability based on porosity.
Industry has relied on the Kozeny equation and empirical studies to establish relationships between macroscopic formation measurements and formation fluid flow characteristics. Kozeny reported that a number of variables not previously considered, including specific surface areas of the pore system, tortuosity, and shape of the pore system, affected the relationship between porosity and permeability. See J. Kozeny, "Uber Die Kapillare Leitung des Wassers im Boden," 136a Sitz. Ber., Akademie Wiss. Wien., Math. Nat. (Abt. IIa) 271 (1927). Using a simple model of a bundle of capillary tubes, Kozeny derived an expression for the relationship between porosity and permeability, as follows: ##EQU1## where k is permeability (cm.sup.2), .phi. is porosity (no units), S.sub.pv is the internal surface area of the pore space per unit of pore volume, and 2 is a constant (the "Kozeny constant"). For unconsolidated formations, Equation 1 becomes: ##EQU2## where S.sub.gv is the specific surface area of a porous material per unit of grain volume. Kozeny's model has gained general acceptance in the industry as a descriptor of the porosity-permeability relationship.
Carman recognized that textural parameters, such as size, sorting, shape, and spatial distribution of grains have a substantial impact on formation permeability. See P. C. Carman, "Fluid Flow Through Granular Beds,"15 Trans. Inst. Chem. Engs. 150 (1937). Carman adapted the Kozeny equation for formations comprised of uniform and homogeneous rocks having a dominance of nearly spherical grains by changing the Kozeny constant from 2 to 5. Carman's adaptation is also a widely used form of the Kozeny equation.
Neither the Kozeny nor the Kozeny-Carman models accurately characterize the relationship between porosity and permeability because reservoir formations never conform to the assumed capillary tube or spherical grain models. The lack of general applicability of the Kozeny and Kozeny-Carman equations led researchers to search for formation-specific empirical correlations between porosity and permeability. Such empirical correlations have been poor, however, and in the absence of plausible physical models to explain the predicted relationships, they have not gained wide acceptance.
A number of researchers have investigated the relationship between well log data and permeability. See M. R. Wyllie & W. D. Rose, "Some Theoretical Considerations Related to the Quantitative Evaluation of the Physical Characteristics of Reservoir Rock from Electrical Log Data," 189 Petroleum Transactions, AIME 105 (1950); W. D. Rose & W. A. Bruce, "Evaluation of Capillary Character in Petroleum Reservoir Rock," 186 Petroleum Transactions, AIME 127 (1949); M. P. Tixier, "Electric Log Analysis in the Rocky Mountains," 48 Oil and Gas Journal 143 (1949); G. E. Archie, "The Electrical Resistivity Log as an Aid in Determining Reservoir Characteristics," 146 Petroleum Transactions, AIME 54 (1942); M. C. Leverett, "Flow of Oil-Water Mixtures Through Unconsolidated Sands," 132 Petroleum Transactions, AIME 149 (1939). These researchers pioneered different correlations relating cementation factor, resistivity index, saturation, permeability, and porosity. Wyllie and Rose also pointed out that these parameters are closely related to the textural parameters of formation rocks expressed in the Kozeny equation and to expressions of capillary pressure phenomena. None of these researchers, however, was able to construct an accurate correlation between porosity and permeability. Each concluded that accurate estimates of reservoir rock parameters should not be made from log data alone, but from a combination of core analysis and log data.
Amaefule, et al. observe that the "mean hydraulic radius" ((k/.phi.).sup.1/2), calculated from permeability and porosity data derived from core sample analysis, relates Darcy flow properties to pore space attributes. See J. O. Amaefule, D. G. Kersey, D. M. Marschall, J. D. Powell, L. E. Valencia, D. K. Keelan, "Reservoir Description: A Practical Synergistic Engineering and Geological Approach Based on Analysis of Core Data," SPE No. 18167 (1988). Amaefule, et al. note that core analysis descriptions can be used to divide the reservoir into various hydraulic units. They use the concept of a mean hydraulic radius to develop relationships between microscopic pore level attributes and macroscopic core data to establish zones with similar hydraulic quality. Amaefule, et al. discuss conceptually the desireability of establishing relationships between core data and well log data, such as porosity, but no such relationships are developed in their paper.
The Kozeny and Kozeny-Carman constants, 2 and 5, are valid only for the capillary tube and spherical grain models, respectively. These models, as previously noted, do not translate accurately to the general case in which the porous media do not conform to the models. In the general case, permeability varies with a variety of characteristics other than porosity, including pore shape and size, grain shape and size, pore and grain distribution, tortuosity, cementation, and type of pore system, that is, intergranular, intercrystalline, vuggy, or fractured. These characteristics vary from one lithology to another and even within formation units of similar lithology. Thus, they cannot be modelled accurately as a constant.
It would be desirable to provide a method for determining the permeability of a formation based on macroscopic data available from a well log. Such a method preferably would take account of variances in permeability as a consequence of pore shape and size, grain shape and size, pore and grain distribution, tortuosity, cementation, and type of pore system.